This article is cited in 1 scientific paper (total in 1 paper)
On basicity of eigenfunctions of second order discontinuous differential operator
B. T. Bilalov, T. B. Gasymov
Institute of Mathematics and Mechanics of NAS of Azerbaijan, 9, B. Vahabzade Str., AZ1141, Baku, Azerbaijan
We consider a spectral problem for a second order discontinuous differential operator with spectral parameter in the boundary condition. We present a method for establishing the basicity of eigenfunctions for such problem. We also consider a direct expansion of a Banach space with respect to subspaces and we propose a method for constructing a basis for a space by the bases in subspaces. We also consider the cases when the bases for subspaces are isomorphic and the corresponding isomorphisms are not needed. The completeness, minimality and uniform minimality of the corresponding systems are studied. This approach has extensive applications in the spectral theory of discontinuous differential operators.
eigenfunctions, basis, completeness, minimality, uniform minimality.
|National Academy of Sciences of Azerbaijan
|This work was supported by the Research Program Competition launched by the National Academy of Sciences of Azerbaijan (Program: Frame theory Applications of Wavelet Analysis to Signal Processing in Seismology and Other Fields).
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Ufa Mathematical Journal, 2017, 9:1, 109–122 (PDF, 391 kB); https://doi.org/10.13108/2017-9-1-109
B. T. Bilalov, T. B. Gasymov, “On basicity of eigenfunctions of second order discontinuous differential operator”, Ufimsk. Mat. Zh., 9:1 (2017), 109–122; Ufa Math. J., 9:1 (2017), 109–122
Citation in format AMSBIB
\by B.~T.~Bilalov, T.~B.~Gasymov
\paper On basicity of eigenfunctions of second order discontinuous differential operator
\jour Ufimsk. Mat. Zh.
\jour Ufa Math. J.
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